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Odd number of pigs in cages
- Thread starter jimoo
- Start date
lionelhill
Technical User
Dian, Pigs might. I think pigs would feel strongly about keeping their integrity; no non-integral pigs allowed. Though they might feel happier about non-integral cages.
Sam Bones, sorry, IT is no longer a safe haven from manual work - hadn't you herd?
Olaf, there are enough angry birds in my life.
Sam Bones, sorry, IT is no longer a safe haven from manual work - hadn't you herd?
Olaf, there are enough angry birds in my life.
CajunCenturion
Programmer
==> 1.5 is considered an odd number?
Only if 1.5 is considered an integer.
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Good Luck
To get the most from your Tek-Tips experience, please read
FAQ181-2886
As a circle of light increases so does the circumference of darkness around it. - Albert Einstein
Only if 1.5 is considered an integer.
--------------
Good Luck
To get the most from your Tek-Tips experience, please read
FAQ181-2886
As a circle of light increases so does the circumference of darkness around it. - Albert Einstein
Here's the output after a small change to my program...
Topology 1: {{P} P} {P} {P}
1. {{
]}} {]]]]]} {]]]}
2. {{]}} {]]]]]]]} {]}
3. {{]}]]} {]]]} {]]]}
4. {{]}]]} {]]]]]} {]}
5. {{]}]]]]} {]]]} {]}
6. {{]}]]]]]]} {]} {]}
7. {{]]]}} {]]]} {]]]}
8. {{]]]}} {]]]]]} {]}
9. {{]]]}]]} {]]]} {]}
10. {{]]]}]]]]} {]} {]}
11. {{]]]]]}} {]]]} {]}
12. {{]]]]]}]]} {]} {]}
13. {{]]]]]]]}} {]} {]}
13 solutions
Topology 2: {{{{P} P} P} P}
14. {{{{]}}}]]]]]]]]}
15. {{{{]}}]]}]]]]]]}
16. {{{{]}}]]]]}]]]]}
17. {{{{]}}]]]]]]}]]}
18. {{{{]}}]]]]]]]]}}
19. {{{{]}]]}}]]]]]]}
20. {{{{]}]]}]]}]]]]}
21. {{{{]}]]}]]]]}]]}
22. {{{{]}]]}]]]]]]}}
23. {{{{]}]]]]}}]]]]}
24. {{{{]}]]]]}]]}]]}
25. {{{{]}]]]]}]]]]}}
26. {{{{]}]]]]]]}}]]}
27. {{{{]}]]]]]]}]]}}
28. {{{{]}]]]]]]]]}}}
29. {{{{]]]}}}]]]]]]}
30. {{{{]]]}}]]}]]]]}
31. {{{{]]]}}]]]]}]]}
32. {{{{]]]}}]]]]]]}}
33. {{{{]]]}]]}}]]]]}
34. {{{{]]]}]]}]]}]]}
35. {{{{]]]}]]}]]]]}}
36. {{{{]]]}]]]]}}]]}
37. {{{{]]]}]]]]}]]}}
38. {{{{]]]}]]]]]]}}}
39. {{{{]]]]]}}}]]]]}
40. {{{{]]]]]}}]]}]]}
41. {{{{]]]]]}}]]]]}}
42. {{{{]]]]]}]]}}]]}
43. {{{{]]]]]}]]}]]}}
44. {{{{]]]]]}]]]]}}}
45. {{{{]]]]]]]}}}]]}
46. {{{{]]]]]]]}}]]}}
47. {{{{]]]]]]]}]]}}}
48. {{{{]]]]]]]]]}}}}
35 solutions
Topology 3: {{P} {P} {P} P }
49. {{]} {]} {]}]]]]]]}
50. {{]]]} {]} {]}]]]]}
51. {{]]]} {]]]} {]}]]}
52. {{]]]} {]]]} {]]]}}
53. {{]]]]]} {]} {]}]]}
54. {{]]]]]} {]]]} {]}}
55. {{]]]]]]]} {]} {]}}
7 solutions
Topology 4: {{{P} {P} P} P }
56. {{{]} {]}]}]]]]]]}
57. {{{]} {]}]]]}]]]]}
58. {{{]} {]}]]]]]}]]}
59. {{{]} {]}]]]]]]]}}
60. {{{]]]} {]}]}]]]]}
61. {{{]]]} {]}]]]}]]}
62. {{{]]]} {]}]]]]]}}
63. {{{]]]} {]]]}]}]]}
64. {{{]]]} {]]]}]]]}}
65. {{{]]]]]} {]}]}]]}
66. {{{]]]]]} {]}]]]}}
67. {{{]]]]]} {]]]}]}}
68. {{{]]]]]]]} {]}]}}
13 solutions
Topology 5: {{{P} P} {P} P }
69. {{{]}} {]}]]]]]]]}
70. {{{]}} {]]]}]]]]]}
71. {{{]}} {]]]]]}]]]}
72. {{{]}} {]]]]]]]}]}
73. {{{]}]]} {]}]]]]]}
74. {{{]}]]} {]]]}]]]}
75. {{{]}]]} {]]]]]}]}
76. {{{]}]]]]} {]}]]]}
77. {{{]}]]]]} {]]]}]}
78. {{{]}]]]]]]} {]}]}
79. {{{]]]}} {]}]]]]]}
80. {{{]]]}} {]]]}]]]}
81. {{{]]]}} {]]]]]}]}
82. {{{]]]}]]} {]}]]]}
83. {{{]]]}]]} {]]]}]}
84. {{{]]]}]]]]} {]}]}
85. {{{]]]]]}} {]}]]]}
86. {{{]]]]]}} {]]]}]}
87. {{{]]]]]}]]} {]}]}
88. {{{]]]]]]]}} {]}]}
20 solutions
![[bigsmile]](/data/assets/smilies/bigsmile.gif "[bigsmile] [bigsmile]")
Topology 1: {{P} P} {P} {P}
1. {{
]}} {]]]]]} {]]]}2. {{
]}} {]]]]]]]} {]}3. {{
]}]]} {]]]} {]]]}4. {{
]}]]} {]]]]]} {]}5. {{
]}]]]]} {]]]} {]}6. {{
]}]]]]]]} {]} {]}7. {{
]]]}} {]]]} {]]]}8. {{
]]]}} {]]]]]} {]}9. {{
]]]}]]} {]]]} {]}10. {{
]]]}]]]]} {]} {]}11. {{
]]]]]}} {]]]} {]}12. {{
]]]]]}]]} {]} {]}13. {{
]]]]]]]}} {]} {]}13 solutions
Topology 2: {{{{P} P} P} P}
14. {{{{
]}}}]]]]]]]]}15. {{{{
]}}]]}]]]]]]}16. {{{{
]}}]]]]}]]]]}17. {{{{
]}}]]]]]]}]]}18. {{{{
]}}]]]]]]]]}}19. {{{{
]}]]}}]]]]]]}20. {{{{
]}]]}]]}]]]]}21. {{{{
]}]]}]]]]}]]}22. {{{{
]}]]}]]]]]]}}23. {{{{
]}]]]]}}]]]]}24. {{{{
]}]]]]}]]}]]}25. {{{{
]}]]]]}]]]]}}26. {{{{
]}]]]]]]}}]]}27. {{{{
]}]]]]]]}]]}}28. {{{{
]}]]]]]]]]}}}29. {{{{
]]]}}}]]]]]]}30. {{{{
]]]}}]]}]]]]}31. {{{{
]]]}}]]]]}]]}32. {{{{
]]]}}]]]]]]}}33. {{{{
]]]}]]}}]]]]}34. {{{{
]]]}]]}]]}]]}35. {{{{
]]]}]]}]]]]}}36. {{{{
]]]}]]]]}}]]}37. {{{{
]]]}]]]]}]]}}38. {{{{
]]]}]]]]]]}}}39. {{{{
]]]]]}}}]]]]}40. {{{{
]]]]]}}]]}]]}41. {{{{
]]]]]}}]]]]}}42. {{{{
]]]]]}]]}}]]}43. {{{{
]]]]]}]]}]]}}44. {{{{
]]]]]}]]]]}}}45. {{{{
]]]]]]]}}}]]}46. {{{{
]]]]]]]}}]]}}47. {{{{
]]]]]]]}]]}}}48. {{{{
]]]]]]]]]}}}}35 solutions
Topology 3: {{P} {P} {P} P }
49. {{
]} {]} {]}]]]]]]}50. {{
]]]} {]} {]}]]]]}51. {{
]]]} {]]]} {]}]]}52. {{
]]]} {]]]} {]]]}}53. {{
]]]]]} {]} {]}]]}54. {{
]]]]]} {]]]} {]}}55. {{
]]]]]]]} {]} {]}}7 solutions
Topology 4: {{{P} {P} P} P }
56. {{{
]} {]}]}]]]]]]}57. {{{
]} {]}]]]}]]]]}58. {{{
]} {]}]]]]]}]]}59. {{{
]} {]}]]]]]]]}}60. {{{
]]]} {]}]}]]]]}61. {{{
]]]} {]}]]]}]]}62. {{{
]]]} {]}]]]]]}}63. {{{
]]]} {]]]}]}]]}64. {{{
]]]} {]]]}]]]}}65. {{{
]]]]]} {]}]}]]}66. {{{
]]]]]} {]}]]]}}67. {{{
]]]]]} {]]]}]}}68. {{{
]]]]]]]} {]}]}}13 solutions
Topology 5: {{{P} P} {P} P }
69. {{{
]}} {]}]]]]]]]}70. {{{
]}} {]]]}]]]]]}71. {{{
]}} {]]]]]}]]]}72. {{{
]}} {]]]]]]]}]}73. {{{
]}]]} {]}]]]]]}74. {{{
]}]]} {]]]}]]]}75. {{{
]}]]} {]]]]]}]}76. {{{
]}]]]]} {]}]]]}77. {{{
]}]]]]} {]]]}]}78. {{{
]}]]]]]]} {]}]}79. {{{
]]]}} {]}]]]]]}80. {{{
]]]}} {]]]}]]]}81. {{{
]]]}} {]]]]]}]}82. {{{
]]]}]]} {]}]]]}83. {{{
]]]}]]} {]]]}]}84. {{{
]]]}]]]]} {]}]}85. {{{
]]]]]}} {]}]]]}86. {{{
]]]]]}} {]]]}]}87. {{{
]]]]]}]]} {]}]}88. {{{
]]]]]]]}} {]}]}20 solutions
Olaf Doschke
Programmer
Now I've also had the time to do a brute force attack on the problem. I was not separating cage topology from the rest of the problem in the same way, but made a brute force attack on the topology too: first I did compute 4 pig counts from 1-9 summing to 9 and put these counts right after a '{', which resulted in a raw solution like {p1{p2{p3{p4, then added 0 to the maximum number of possible cage closings '}' at each position.
I end up with only 74 solutions:
Will check within the next few days, which solutions I am missing.
Bye, Olaf.
I end up with only 74 solutions:
Code:
1 {1{1}{2{5}}}
2 {1}{1}{2{5}}
3 {1{1}{4{3}}}
4 {1}{1}{4{3}}
5 {1{1}{6{1}}}
6 {1}{1}{6{1}}
7 {1{2{1}}{5}}
8 {1}{2{1}}{5}
9 {1{2{3}}{3}}
10 {1}{2{3}}{3}
11 {1{2{5}}{1}}
12 {1}{2{5}}{1}
13 {1{3}{2{3}}}
14 {1}{3}{2{3}}
15 {1{3}{4{1}}}
16 {1}{3}{4{1}}
17 {1{4{1}}{3}}
18 {1}{4{1}}{3}
19 {1{4{3}}{1}}
20 {1}{4{3}}{1}
21 {1{5}{2{1}}}
22 {1}{5}{2{1}}
23 {1{6{1}}{1}}
24 {1}{6{1}}{1}
25 {2{1{1}{5}}}
26 {2{1}{1}{5}}
27 {2{1}}{1}{5}
28 {2{1{3}{3}}}
29 {2{1}{3}{3}}
30 {2{1}}{3}{3}
31 {2{1{5}{1}}}
32 {2{1}{5}{1}}
33 {2{1}}{5}{1}
34 {2{2{2{3}}}}
35 {2{2{4{1}}}}
36 {2{3{1}{3}}}
37 {2{3}{1}{3}}
38 {2{3}}{1}{3}
39 {2{3{3}{1}}}
40 {2{3}{3}{1}}
41 {2{3}}{3}{1}
42 {2{4{2{1}}}}
43 {2{5{1}{1}}}
44 {2{5}{1}{1}}
45 {2{5}}{1}{1}
46 {3{1}{2{3}}}
47 {3}{1}{2{3}}
48 {3{1}{4{1}}}
49 {3}{1}{4{1}}
50 {3{2{1}}{3}}
51 {3}{2{1}}{3}
52 {3{2{3}}{1}}
53 {3}{2{3}}{1}
54 {3{3}{2{1}}}
55 {3}{3}{2{1}}
56 {3{4{1}}{1}}
57 {3}{4{1}}{1}
58 {4{1{1}{3}}}
59 {4{1}{1}{3}}
60 {4{1}}{1}{3}
61 {4{1{3}{1}}}
62 {4{1}{3}{1}}
63 {4{1}}{3}{1}
64 {4{2{2{1}}}}
65 {4{3{1}{1}}}
66 {4{3}{1}{1}}
67 {4{3}}{1}{1}
68 {5{1}{2{1}}}
69 {5}{1}{2{1}}
70 {5{2{1}}{1}}
71 {5}{2{1}}{1}
72 {6{1{1}{1}}}
73 {6{1}{1}{1}}
74 {6{1}}{1}{1}Will check within the next few days, which solutions I am missing.
Bye, Olaf.
One missing solution that's easy to spot is the one with all nine pigs in an innermost cage: {{{{9}}}}. More generally, it appears that all of your solutions have at least one pig in each cage. This is a requirement if the cage is standing alone, but a cage that contains nested cages can get all its pigs from the inner cages. So there is no requirement that an outer cage in a nest contain a separate quota of pigs.
lionelhill
Technical User
Sam, all your pigs are facing us. For artistic reality, they should be at random angles.
Olaf Doschke
Programmer
Thanks, yes, I simply should also consider 0. This is how Sam Bones did make all his solutions the same string length. I should have looked closer there. Yes, and I did not yet remove permuations.
Bye, Olaf.
Bye, Olaf.
Olaf Doschke
Programmer
Ok, now I'm at 175 solutions including 0 in my nomenclature. Permutations should account for 87 of these solutions to be double solutions. {0{0{0{9}}}} surely is one solution without a permutation.
So, yes, separating cage topologies surely does simplify finding the distinct different solutions.
Bye, Olaf.
So, yes, separating cage topologies surely does simplify finding the distinct different solutions.
Bye, Olaf.
One of the ways I removed permutations is if there were two unnested cages, I would only print it if cage 1 was >= cage 2. That is...
{P1} >= {P2}
That means these would print...
{5} {1}
{3} {3}
...but this would not...
{1} {5}
That effectively removes the unnested cage dupes due to order.
I didn't have dupes like {1}{1}{6{1}} and {6{1}}{1}{1} because I hardcoded the topologies.
{P1} >= {P2}
That means these would print...
{5} {1}
{3} {3}
...but this would not...
{1} {5}
That effectively removes the unnested cage dupes due to order.
I didn't have dupes like {1}{1}{6{1}} and {6{1}}{1}{1} because I hardcoded the topologies.
Olaf Doschke
Programmer
Thanks, Sam.
That's how I'd approach this, too. Sorting is always a good way to reveal permutations.
Bye, Olaf.
That's how I'd approach this, too. Sorting is always a good way to reveal permutations.
Bye, Olaf.
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